Metamorphic aerial robot capable of mid-air shape morphing for rapid perching

Aerial robots can perch onto structures at heights to reduce energy use or to remain firmly in place when interacting with their surroundings. Like how birds have wings to fly and legs to perch, these bio-inspired aerial robots use independent perching modules. However, modular design not only increases the weight of the robot but also its size, reducing the areas that the robot can access. To mitigate these problems, we take inspiration from gliding and tree-dwelling mammals such as sugar gliders and sloths. We noted how gliding mammals morph their whole limb to transit between flight and perch, and how sloths optimized their physiology to encourage energy-efficient perching. These insights are applied to design a quadrotor robot that transitions between morphologies to fly and perch with a single-direction tendon drive. The robot’s bi-stable arm is rigid in flight but will conform to its target in 0.97 s when perching, holding its grasp with minimal energy use. We achieved a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$30\%$$\end{document}30% overall mass reduction by integrating this capability into a single body. The robot perches by a controlled descent or a free-falling drop to avoid turbulent aerodynamic effects. Our proposed design solution can fulfill the need for small perching robots in cluttered environments.


Supplementary
Distance between rigid links (hinge gap) C 10 Elastic constant of latex membrane C 01 Elastic constant of latex membrane λ Membrane stretch ratio (current/unstretched) λ 0 Initial stretch ratio (at manufacturing)

Deflection of the morphing robotic arm
Approximating the quad-rotor arms as Euler-Bernoulli cantilever beams during flight, we derive vertical deflection z as a function of where T is the thrust of the rotor, L the length of the arm, and the distance from the root of the arm x (Supplementary Table S(1)). The stiffness of the arm (EI) arm , due to the sandwich construction, is bounded by two analytical models. As the arm is comprised of a series of polyimide joints, the lower bound stiffness model assumes that the load is carried by a homogeneous polyimide structure. However, the neutral axis of bending is imposed on the top plane as the carbon fiber plates, magnitudes higher in Young's modulus, will restrict the compression. Further assuming that second order and higher terms of the thickness, t k and t cf , are insignificant, this gives The upper bound model assumes a homogeneous carbon fiber structure. With the neutral axis of bending imposed at the centroid of the cross section, this gives We can further model the arm as connected homogeneous sections, alternating between polyimide and carbon fiber, giving equations in the form and X i = i 0 l i .

Parametric numerical study of the tendon actuation
The transition dynamics from the locked to unlocked state is determined by the characteristics of the servomotor-spool, the elastic elements, the polyimide hinges, and the tendon anchor position (Supplementary Figure S(1)). The servomotor is modelled as a DC motor with a linear speed-torque curve such that The speed of the arm unfolding is estimated by a forward euler numerical scheme with the servo angular rate (θ) determined by the torque (τ ) at each time step. Using a Mooney-Rivlin model, assuming the membrane to be incompressible (Poisson ratio= 0.5), the stress of the membrane, σ is with the stretch ratio (λ) defined as the length ratio of the stretched and unstretched membrane length. Thus which for the geometry of the prototype The moment due to the stiffness of the polyimide hinge M joint is modelled as an Euler-Bernoulli beam of uniform curvature where is the strain The moment equilibrium at the hinge gives assuming frictionless tendon motion. F t denotes the tension of the tendon, the force of the membrane F m = σw m t m , β the angle between the tendon and the side links of the arm, and m the length of the tendon between the side links and the tendon pivot. The angle between the sections of the arm (α) is formulated as a function of the servo angle (θ), where θ = 0 is the neutral state of the arm in flight configuration. The tension of the tendon is further multiplied eightfold by the number of actuated tendons on an arm pair and the pulley system. The torque required is formulated as a function of the servo angle (θ) (see Fig.2) where definitions are given in table S(1). Finally, (19) can be substituted into (8) and numerically advanced in time to determine the position of the arm.
A parametric study was conducted to determine the trade-offs between actuation speed and servomotor limits. Predictably, the opening time increased with increasing membrane thickness and stretch, and decreased with increasing hinge thickness. However, the servomotor's torquespeed characteristics and spool manufacturing constraints result in an optimum spool radius limited by hardware.

Video analysis
The transition times between the three configurations on the prototype robots are determine by video analysis. During this analysis, the robots are rigidly mounted to a test frame. While the folding and unfolding speeds vary due to the variances in the manufacturing, the robots are able to achieve locked-to-unlocked times of less than 1s. A further 0.25s is required for both the unlocked arms to sweep pass π/2. The flight behaviours of the robot during perching transition was further examined with high speed video. The high speed video was captured with an Apple iPhone 11 Pro. The platform, while in a semi-flexible state in mid-transition, was sufficiently rigid to exert some stabilizing forces. Thus, the perching transition can begin prior to motor cutoff, reducing the glide time.

Robot mass breakdown
The mass breakdown of the prototype robot is as shown in Supplementary Table S(2).

Tip deflection data analysis
The deflection of the arm tip is tested using weights hung from the arm tip. This test approximates thrust loading from the rotor. The load is fully taken off the arm each time before a new load is applied (Fig. S(2)). The weight was gently applied to ensure no effects from momentum. To denoise the data from motion capture, the z displacement was low pass filtered. A sliding window peak and trough finding algorithm finds the deflection at zero load and full load at each load cycle.

Flight testing and data analysis
The T265 camera was mounted on the platform during all perching tests. However, during outdoor testing using the camera's visual inertial odometry, we found that the VIO output drifts significantly in the absence of contrasting and angular objects. This issue was confirmed qualitatively with flight tests in four settings; indoor, forest understory, grass land, grass land with a scattering of man-made objects.